[Verse 1]
When integers cluster in narrow domains
Standard sorting algorithms strain their chains
But counting sort cuts through with elegant grace
No comparisons needed, just allocate space
Count each value's frequency, store in array
Map every digit to its rightful display
[Chorus]
Count the frequencies, build the scaffold high
Cumulative sums reveal where digits lie
Linear time complexity when range stays tight
Counting sort transforms chaos into sight
O of n plus k, memory's the price
Stable and swift when the range rolls dice
[Verse 2]
Initialize counters, zero fills the slate
Traverse input once, let frequencies accumulate
Transform counts to positions with prefix math
Each bucket holds the key to sorting's path
Walk backwards through original sequence flow
Stability preserved as sorted numbers grow
[Chorus]
Count the frequencies, build the scaffold high
Cumulative sums reveal where digits lie
Linear time complexity when range stays tight
Counting sort transforms chaos into sight
O of n plus k, memory's the price
Stable and swift when the range rolls dice
[Bridge]
When k explodes beyond reasonable bounds
Counting sort drowns in memory's grounds
But small domains unleash its truest power
Radix sort's backbone in its finest hour
Non-comparative excellence takes the stage
Integer sequences bow to counting's rage
[Outro]
From frequencies to positions, logic flows
Three passes through and perfect order shows
When range constrains the values in your set
Counting sort delivers without regret